As for "how do they do the timetables?", more what they did than how they figured them out. The modern local ones look to have been knocked up in Word
well, since you asked...
traditionally, they would start hand-written and end up typeset to that operator's house style - possibly once for timetable books, once for roadside timetable displays, then there would need to be an extract for the bus crew to work to (the style and terminology would vary, but either a time card / running board with just what that bus is doing, or a duty card with just what that crew is doing), a 'run out sheet' for buses so the garage engineering staff know how many buses are needed, at what times, what order they need to leave the garage in and how many miles each bus is scheduled to do, a signing-on sheet for crews so that the 'output' supervisors knew that crews had arrived for work on time (and would do something if they didn't) then something for the bus station or roadside inspectors to refer to - possibly departure sheets for key locations, or a version of the timetable showing the bus workings and crew duties.
The crew duties would then need fitting in to rotas which again would need to be displayed at the garage for crews' and supervisors' use, and the pay clerk/s would need copies of all this, along with the details of each duty (as in duty 123 is 7 hours 45 pay plus 15 minutes spreadover allowance plus 45 minutes unsocial hours allowance and so on.)
The level of 'typesetting' would vary - some smaller operators were still at the typewriter and duplicator level of tech in to the 1990s.
there's some live timetables / schedules office action in
this film clip (an extract from british transport films 'all that mighty heart') from 0.42 to 1.05 (the man drawing diagonal lines is constructing a crew duty schedule on a graph that's got the bus workings on - somewhere, i've got a small amount of schedules graph paper with the horizontal axis being time - when i started, computerised scheduling was still only done at the largest of operators.)
In the current era, much of this is based on electronic data - there's a handful of companies who do software for this (obviously it's a bit niche / specialised) - while these products tend not to be quite as great as the software companies say, the big difference is that one lot of data is used for multiple purposes, and the same data isn't being re-typed (with a risk of errors each time) several times, and (in theory) you just press different buttons to get all the different versions once you've constructed timetable / duty schedule / rota.
And it can all be joined up with the driver pay system - drivers can see their duties for the next few weeks on their smart phones, they can clock on and off automatically at the depot with their smart card or whatever, and the system will know that driver J Smith is on duty 123 today, and know if they have booked on at the right time, the controllers will only get an alert if they don't, rather than having to tick names off a list. (some operators - particularly where drivers aren't handling cash - are going down the path of drivers being able to book on / off remotely via app or text message on duties where they don't bring a bus from or two depot - the merits of this are subject to some debate.)
The tech of course can cause issues - one place I worked, the schedules system and the pay system handled the concept of midnight differently, and in the end we had to make a manual adjustment to any duty that naturally booked on or off duty at exactly midnight, so that they would either finish at 0001 or start at 2359, otherwise it would cock their pay up.
Most of these products can generate printed timetables / departure lists for roadside timetables, although they tend not to be great at producing printable timetables in traditional format, and there are a few specialist firms who do that sort of thing - again, they generally get the data electronically. The smallest of operators will produce something in Excel or Word, though.
There is
a standardised file format for bus timetables, which is used to feed in to the government's
BODS data set and regional Traveline systems, as well as feeding real time passenger information systems and electronic ticket machines, so again it's all the same base data being used. It's also now done to 'stop level' (as in every single bus stop is in the data - even the 'imaginary' bus stops where there's nothing there to show it's a bus stop but buses will stop there) rather than 'timing point' level where maybe one stop in 10 would be listed. In turn, third party websites (e.g. google maps, bustimes) get and use this data.
In some areas, local councils are involved in producing roadside timetables and / or printed timetables (either for tendered services or across the board) and will (generally) use operators' electronic data to do this rather than start from scratch.
Although in practice it tends to need a bit of checking and arguing (small to medium sized operators may not have the tech skills to handle the software, and the big operators tend to concentrate the people who do at regional offices, and they may not have the detailed local knowledge.) The very smallest operators (particularly the community transport sector) tend to get someone to do the electronic stuff for the - again this may be the local council.
It's fair to say (and perhaps not recognised enough at DFT level) that the requirements on operators to do all the electronic stuff (and have the tech kit on buses) has pushed some small operators out of doing local bus / stage carriage service, when in the past they used to do a school contract and then a few 'market day' bus routes with the same vehicle and driver. As with the (worthwhile) requirement for low floor / accessible buses, the question of funding it all - particularly in rural areas - was never really thought through properly.
Obviously the above is a brief summary...
For one-off heritage bus running day events, most people doing that don't have access to schedules software and those who do mostly probably won't have employer's permission to use it for something outside work, so it tends to be paper and Word / Excel or similar. I've got templates in Excel that are close to what a lot of bus operators' 1950s or 1960s timetable books looked like, for example, and I try to stick as far as I can to the principle of one master file, and just re-format the same data for the various formats it needs printing in.